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0:09

Многоскоростные системы

0:43

Изменение частоты дискретизации

1:37

Понижение частоты дискретизации в M-раз

4:03

Повышение частоты дискретизации в L-раз

Основы ЦОС: 17. Частотное представление сигнала (скачивание скриптов в описании)

Основы ЦОС: 17. Частотное представление сигнала (скачивание скриптов в описании)

Channel: ЦИТМ Экспонента

Основы ЦОС: 14. Статистическая обработка сигнала (ссылки на скачивание скриптов в описании)

Основы ЦОС: 14. Статистическая обработка сигнала (ссылки на скачивание скриптов в описании)

Channel: ЦИТМ Экспонента

Основы ЦОС: 09. Синусоидальный сигнал как базис (ссылка на скачивание скрипта в описании)

Основы ЦОС: 09. Синусоидальный сигнал как базис (ссылка на скачивание скрипта в описании)

Channel: ЦИТМ Экспонента

Основы ЦОС: 04. Знакомство с MATLAB (ссылки на скачивание скриптов в описании)

Основы ЦОС: 04. Знакомство с MATLAB (ссылки на скачивание скриптов в описании)

Channel: ЦИТМ Экспонента

SimMechanics

SimMechanics

Channel: ЦИТМ Экспонента

многоскоростные системы

многоскоростные фильтры

интерполяция

децимация

upsampling

downsampling

MATLAB

Simulink

ЦОС

цифровая обработка сигналов

DSP

матлаб

симулинк

многоскоростные_системы

многоскоростные_фильтры

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multi-speed systems; the Russian

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established definition is a little confusing; it

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immediately seems like a system that

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can run at once at a speed; in

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fact, this is just a translation of the term

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multi-raid, which alludes specifically to

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different signal sampling rates in a

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technically multi-speed system can

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be called a digital system that

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operates with several signals with different

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frequencies, for example, a

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signal with frequency f 1 and a signal with

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frequency f 2 pass through the system;

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they also exit inside; they are

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somehow independently processed;

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this is the so-called system with

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independent frequencies, but they are not of

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greatest interest to us,

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but the main focus of this and the following

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video, these are systems that change the

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sampling frequency, the general diagram of the simplest

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system is the signal at the input with one

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sampling frequency, the signal at the output with another

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sampling frequency,

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if the sampling frequency is reduced,

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we call it

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down sampling and up to 7

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decimation, to which this can be applied,

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for example, you have a purchased cp which

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you use to digitize someone's

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relatively slowly changing

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analog signal in this case the

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data flow becomes redundant there is

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no need to store data with such accuracy

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so to save sample resources

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you can thin out if the frequency increases

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then we are talking about absinthe lings and

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interpolation A similar operation

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is used when you need, for example,

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to combine discrete data with another

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set of more densely recorded data

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that predicts on one time scale,

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or we need to increase the resolution or

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accuracy of data representation.

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Let's get acquainted with these processes using

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simple examples when the frequency changes

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by an integer number of times decrease

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sampling frequency into an integer, for example, as

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we indicated here in m 1, this is the decimation of

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samples in the output signal, we leave

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only each smart sample, we

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throw out the rest in the picture, an example of reducing the

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sampling frequency of a harmonic

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signal by three times, only

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every third report of the sequence remains, I

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described a process called down

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sampling mercy, one problem, we may

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not comply with Kotelnikov’s theorem,

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in fact we are sampling

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the signal over another discrete

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time scale due to the effect and

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lessing, we may lose data from the

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initially strong calculations will not

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work in more detail about this, I

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talked about this in a video dedicated to

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Kotelnikov’s theorem,

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so in practice

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doce matsa operations are used, that is, thinning

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with pre-filtering to

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ensure compliance with the conditions of

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Kotelnikov's theorem.

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Consider an example of lowering the frequency of

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matlab signals. In this script, we first

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generate the original signal as the sum of 2 sine

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with frequencies of 1000 hertz and 3400 hertz and

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then lowering the feeling. lization by an

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integer number of times the original lization frequency is

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30 kilohertz let's look at the signal in the

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time and frequency domains and also

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listen to the spectrum of the signal we

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observe clear Beijing 1000 and 3000 400

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hertz now our task is to lower the

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sampling frequency let's do it three times by a

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down factor equal to three and first

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we will do a reduction that the children seem to use the

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down sample methods

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and then with the ds smith command by ear there is

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no difference the reports in time do not

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differ in aspects the peak is observed at

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frequencies of one thousand three thousand 400 hertz

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we lowered the sampling frequency to

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ten kilohertz

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zone bosses that is, the

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sampling frequency fell into in our case,

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it is limited to five kilohertz themselves, but

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what happens if we lower the

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sampling frequency by six times, the

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nike growth zone will shift by two and a

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half kilohertz, what will happen is a

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signal of 3,400

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due to the lifting effect,

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it turns into a signal of 1600 Hz,

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non-compliance with Kotelnikov’s theorem, we

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observe both on the spectrum of the signal and

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when listening, but the dice command

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performs a preliminary

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filtering of the signal, so the

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resulting zone finally includes

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only those signals

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whose frequency does not exceed half the

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sampling frequency of the output signal

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and we will hear a pure tone of 1000 hertz.

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Now let's look at techniques for

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increasing the signal sampling frequency;

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this process is a little more interesting processes of

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lowering the frequency because when lowering

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we threw out the real reports with the signal and

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left something of the signal, where should

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we get the report if we want to increase

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the frequency and d 1 let's start with a process

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called sampling, this is simply

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placing an integer number of zeros between the real calculations of the

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original signal a

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simple way,

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you can also repeat signal reports, this

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process is called ripit, you

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really are implementing it is not much

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more complicated than inserting zeros, but both of these

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methods seriously distort the

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signal shape and often this is unacceptable,

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so you need to use interpolation,

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that is, this count and the values of which we

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approximate based on real data the

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chosen algorithm, mathematical

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methods for interpolating discrete data are

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described in sufficient detail in matlab, but

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when we talk about SOS systems,

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this process is not so simple and how

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interpolation is implemented in practice, we will

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talk in the next video, but for now,

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let's look at examples of increasing the

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sampling frequency of a harmonic

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signal life script original

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sinusoid signal with a main frequency of 1000 hertz

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and a sampling frequency of 8000 hertz,

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let's look at it in the time frequency

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domain and also listen to the spectrum,

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we observe one clear peak in the region of

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1000 hertz and the spectrum observation area

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is limited to four kilohertz,

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now let's raise the

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sampling frequency three times using the absinthe method

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between samples the signals will appear 0 and

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the sound will be distorted,

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but the most interesting things we see are on the

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signal spectrum. I mentioned that the spectrum of a

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discrete signal is periodic and

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by raising the sampling frequency we have

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expanded the Nyquist zone three times,

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now the spectrum contains frequencies from

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0 to 12 kilohertz and we are clearly observing

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spectral copies at frequencies 7 and 9

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kilohertz spectrum of the mirror on the 8 kilohertz band

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and repeats with a period of 8 kilohertz this is

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exactly the value of our

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sampling frequency of the resulting spectral

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copies and gives us three audio someone

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that distorts our audio

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now let's look at the ripit method

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repeating reports also distorts the shape of the

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sine wave but to a lesser extent than from

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adding zeros the signal is a little more

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similar to that of 1 kilohertz

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in the time domain it has fewer

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sharp changes and spectral copies at

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7 9 camp cyclic turns out to be suppressed

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relative to one kilohertz but

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the only way to get a single tone at an

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increased sampling rate

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is interpolation will allow us

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to obtain approximate values between the

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real input signal reports,

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but the shape of the interpolated sinusoid does

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not look distorted on the spectrum, we

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observe one peak and the signal

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is indistinguishable from the original one, and in the next

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video we will talk about

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how we obtained intermediate

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values during interpolation and how do we

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change the sampling rate to a

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fractional value stay on the channel

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Российская платформа математических вычислений и динамического моделирования Engee: сайт: https://start.engee.com/ Телеграм канал: https://t.me/engee_com ############### Наш тренинг "Проектирование систем цифровой обработки сигналов" https://exponenta.ru/SLBE-G В данном видео мы начинаем знакомство с многоскоростными системами, и рассматриваем такие операции, как понижение и повышение частоты дискретизации сигнала в целое число раз. Все видео и описание https://exponenta.ru/news/cifrovaya-obrabotka-signalov Ссылки на скачивание скриптов и файлов данных: https://github.com/ETMC-Exponenta/DSP_YoutubePlaylist/tree/master/multirate Плейлист "Введение в цифровую обработку сигналов (ЦОС)": https://www.youtube.com/playlist?list=PLmu_y3-DV2_kpP8oX_Uug0IbgH2T4hRPL Мы Вконтакте: https://vk.com/mathworks

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